Chapter 7.5, Problem 83PE

(a)

To determine

The system of inequality which defines the condition that there is at least $5$ nights’ stay. At least one night should be spent at a large resort which costs average $\$200$ per night and small inns costs average $\$100$ per night. The budget is not more than $\$700$ per lodging.

(b)

To determine

To graph: The sketch of the system of inequalities $\{\begin{array}{l}200x+100y\le 700\\ x+y\ge 5\\ x\ge 1\end{array}$ as computed in the part (a).

(c)

To determine

The maximum number of nights that can be spent in large resorts within the budgetwhere the condition is that there is at least $5$ nights’ stay. At least one night should be spent at a large resort which costs average $\$200$ per night and small inns costs average $\$100$ per night. The budget is not more than $\$700$ per lodging.